What is the limit as x approaches infinity of 2/x-6 ?

The limit as x approaches infinity of 2/x-6 is -6

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limit as x approaches infinity of 2/x-6

x \to \infty lim (\frac{2}{x} - 6)

- 6

Solution steps

x \to \infty lim (\frac{2}{x} - 6)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (\frac{2}{x}) - x \to \infty lim (6)

x \to \infty lim (\frac{2}{x}) = 0

x \to \infty lim (6) = 6

= 0 - 6

Simplify

= - 6

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What is the limit as x approaches infinity of 2/x-6 ?
The limit as x approaches infinity of 2/x-6 is -6